First of all, let's recap how TOTP works: your authenticator app stores "TOTP password" in an accessible way (some apps store it plaintext, Aegis stores them in an encrypted DB. They can also be stored on Yubikey.). To generate one time code, the app takes the password, concatenates it with current time rounded to 30 seconds and compute a hash from this string.

The resulting hash is used to create a 6 digit code, that you'll enter on login.

To check the code, server repeats the same procedure and compare your result with the just generated one.

As you can see, for this system to work you and the server must use the same hash function.

Conclusion: 1)Hash function in TOTP has nothing to do with password storage, it is used only for TOTP-code generation. 2) Cryptographic security of the hash function is not much a concern here: TOTP code expose an extremely low amount of information about TOTP password, so to reliably recover the password from TOTP-codes you'll have to intercept millions of them.